2D Navier-Stokes Equations Solver for 2D Open Channel Flow

July 8, 2025 · View on GitHub

Introduction

This solver, developed in Fortran 2008, solves the 2D Navier-Stokes Equations for a fluid flowing in an Open-Channel which can be thought of as a river.
The Finite Volume Method (FVM) has been used to discretisise the 2D Navier-Stokes Equations.
The solver has been parallelised using coarrays and the resulting Algebraic Equations from discretisation are solved via the Successive Over Relaxation Method (SOR).
The problem-domain is divided up using Domain Decomposition.

This is a computational technique used to solve large-scale problems - especially partial differential equations (PDEs) — by breaking down the computational domain into smaller subdomains.
Each subdomain is then solved (often in parallel), and the results are combined to obtain the global solution.

The overall problem domain (e.g., a mesh in FEM or grid in FDM) is divided into smaller parts. This can be done geometrically or based on graph partitioning.

Each subdomain is treated as an independent problem, often solved using local solvers.
Communication between neighboring subdomains ensures consistency across interfaces.

Domain decomposition is widely used in parallel computing, as each subdomain can be assigned to a different processor or thread.

Solutions at the boundaries of subdomains must be matched (e.g., using iterative methods like Schwarz methods or Lagrange multipliers) to ensure global consistency.

Overlapping (e.g., Schwarz methods): Subdomains may overlap; iterative data exchange improves convergence.
Non-overlapping (e.g., Schur complement methods, FETI, BDDC): Subdomains meet at interfaces, requiring global interface solvers.

Modern Fortran: Building Efficient Parallel Applications by Milan Curcic.